JERUSALEM (Reuters) - Israelis voted on Tuesday in an election widely expected to win Prime Minister Benjamin Netanyahu a third term in office, pushing the Jewish State further to the right, away from peace with Palestinians and towards a showdown with Iran.

Netanyahu has vowed to pursue the settlement of lands seized during the 1967 Middle East war if he stays in power, a policy that would put him at odds with his international partners and worsen already tense ties with U.S. President Barack Obama.

Polls predict Netanyahu's Likud party, which has forged an electoral pact with the ultra-nationalist Yisrael Beitenu group, will take the most seats in the parliamentary election, albeit considerably fewer than they had originally hoped.

"We want Israel to succeed, we vote Likud-Beitenu ... The bigger it is, the more Israel will succeed," Netanyahu said after casting his ballot alongside his wife and two sons.

Some 5.66 million Israelis are eligible to vote, with polling stations staying open until 10 p.m. Full results are due by Wednesday morning, opening the way for coalition talks that could take several weeks to wrap up.

No Israeli party has ever secured an absolute majority, meaning that Netanyahu, who says that dealing with Iran's nuclear ambitions is his top priority, will have to bring various allies onboard to control the 120-seat Knesset.

The former commando has traditionally looked to religious, conservative parties for backing and is widely expected to reach out to the surprise star of the campaign, self-made millionaire Naftali Bennett who heads the far-right Jewish Home party.

Bennett's youthful dynamism has struck a chord amongst Israelis, most of whom no longer believe in the possibility of a Palestinian peace deal, and has eroded Netanyahu's support base.

Surveys suggest he may take up to 14 seats, many at the expense of Likud-Beitenu, which was projected to win 32 in the last round of opinion polls published on Friday -- 10 less than the two parties won in 2009 when they ran separate lists.

Such a result might embarrass Netanyahu, but would still leave him in pole position to form the next government. Acknowledging the threat, Netanyahu's son Yair urged young Israelis not to abandon the old, established Likud.

"Even if there more trendy parties, there is one party that has a proven record," he said on Tuesday after voting.

Portraying himself as a natural partner for the prime minister, Bennett has alarmed those who want to see an independent Palestinian state created alongside Israel, by calling for the annexation of chunks of the occupied West Bank.

"I pray to God to give me the power to unite all of Israel and to restore Israel's Jewish soul," Bennett said on Monday at a final campaign appearance before Jerusalem's Western Wall.

However, some political analysts have speculated that Netanyahu might seek to project a more moderate image for Israel on the world stage and look to share power with centrist parties, such as Yesh Atid (There is a Future) - a newly formed group led by former TV host Yair Lapid.

ARAB UPRISING

Israel's main opposition party, Labour, which is seen capturing up to 17 seats, has already ruled out a repeat of 2009, when it initially entered Netanyahu's cabinet, promising to promote peace negotiations with the Palestinians.

U.S.-brokered talks collapsed just a month after they started in 2010 following a row over settlement building, and have laid in ruins ever since. Netanyahu blamed the Palestinians for the failure and says his door remains open to discussions.

Palestinian President Mahmoud Abbas says he won't return to the table unless there is a halt to settlement construction.

That looks unlikely, with Netanyahu approving some 11,000 settler homes in December alone, causing further strains to his already notoriously difficult relations with U.S. President Barack Obama, who was sworn in for a second term on Monday.

Tuesday's vote is the first in Israel since Arab uprisings swept the region two years ago, reshaping the Middle East.

Netanyahu has said the turbulence - which has brought Islamist governments to power in several countries long ruled by secularist autocrats, including neighboring Egypt - shows the importance of strengthening national security.

If he wins on Tuesday, he will seek to put Iran back to the top of the global agenda. Netanyahu has said he will not let Tehran enrich enough uranium to make a single nuclear bomb - a threshold Israeli experts say could arrive as early as mid-2013.

Iran denies it is planning to build the bomb, and says Israel, widely believed to have the only nuclear arsenal in the Middle East, is the biggest threat to the region.

The issue has barely registered during the election campaign, with a poll in Haaretz newspaper on Friday saying 47 percent of Israelis thought social and economic issues were the most pressing concern, against just 10 percent who cited Iran.

One of the first problems to face the next government, which is unlikely to take power before the middle of next month at the earliest, is the stuttering economy.